Answer:
24 feet
Step-by-step explanation:
12 ÷ 18=16/y
2y=3*16
y=24
What is the domain? I need help on this problem
The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x ≥ -6
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
\(f(x) = \sqrt{\frac{1}{3}x + 2\)
Set the radicand greater than or equal to 0
So, we have
1/3x + 2 ≥ 0
Next, we have
1/3x ≥ -2
So, we have
x ≥ -6
Hence, the domain of the function is (d) x ≥ -6
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When solving for x, the sine of 33º is used. What other angle and trigonometric function could be used to solve for x? a. cos 57º c. tan 57º b. tan 33º d. cos 33º
hurry
Answer:
The answer is A.Cos 57.
Step-by-step explanation:
Took the test..
60 is 0.4% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 60 , slightly less than 60 , slightly greater than 60 , or a lot greater than 60 ? Explain.
Answer:
15000
Step-by-step explanation:
0.4%=0.004
0.004x=60
x=60/0.004
x=15000
The number 60 is 0.4 percentage of the number 15,000
Given data ,
To find the number that 60 is 0.4% of, we can set up the equation:
60 = 0.4 percentage of x
To solve for x, we need to convert 0.4% to its decimal form, which is 0.004:
0.004 * x = 60
Now we can solve for x by dividing both sides of the equation by 0.004:
x = 60 / 0.004
Dividing 60 by 0.004 gives us:
On simplifying the equation , we get
x = 15,000
Therefore, 60 is 0.4% of 15,000.
Since 0.4% is a very small percentage (less than 1%), we would expect the answer to be a lot greater than 60. This is because when a small percentage is applied to a number, the result will be significantly larger than the original number. In this case, the number that 60 is 0.4% of is 15,000, which is a lot greater than 60.
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Help! 100 points! I'm also giving brainiest to whoever gives a correct answer to the following questions or nonetheless a solid explanation behind their answer. Thank you and comment for any concerns or issues!
Step-by-step explanation:
1a)
it means that after 14 hours into the experiment the temperature of the liquid reaches exactly the temperature of the surrounding room at that moment : 10° F.
1b)
it is the point (14, 10), and I know, because both lines touch or cross each other at that point, as due to the equality relation both curves contain this point (meaning they have the same result value 10 for the same function argument 14).
4a)
because the slope of the line segment at the end is larger (making the line go up at a much steeper angle) than fire the line segment at the beginning.
4b)
it looks like the experiment started at hour 0 with the liquid being at around -5° F.
and it reached +10° F after about 10 hours.
the x (time) difference is +10 (from 0 to 10).
the y (temperature) difference is +15 (from -5 to 10).
so, the slope at the beginning of the excitement is about +15/+10 = 3/2.
and at the end of the experiment it looks like the last line segment starts at about 20 hours with the liquid at about -3° F. and it ends at hour 30 and at 30°F.
the x (time) difference is +10 (from 20 to 30).
the y (temperature) difference is +33 (from -3 to 30).
so, the slope at the end of the excitement is about +33/+10, which is much bigger than 15/10 at the beginning.
Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures 14.8 m 3 ✓ Choo *4.8 Txa 14. $10.25 Choose... 0.05 L Choose 1.000 g/ml Choose.. 6200 cm Choose... 403 kg Choose Figures 14.8 m 3 Choose... $10.25 ✓ Choose... 10.35 10,2% 1x.25 NO.25 0.05L Choose. 1.000 g/ml Choose 6200 cm Choose. Choose.. 403 kg place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m 3 Choose... $10.25 Choose... II 0.05 L ✓ Choose.. 0.x5 x.05 0.0x 1.000 g/mL Choose... 6200 cm Choose... 403 kg Choose... Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... 0.05 L Choose... 1.000 g/mL Choose 1.00 1.0x0 X.000 1.200 Choose... 6200 cm Choose.. 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... Choose... 0.05 L Choose... 1.000 g/ml 6200 cm ✓ COD Bx00 x200 620x 6220 Choose 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures Choose... 14.8 m 3 $10.25 Choose... Choose... 0.05 L 1.000 g/mL Choose.. Choose... 6200 cm 403 kg ✓ Choose XO3 40% 4x3
The table shows the estimated digit and significant figures of each measurement and their representation with x.
Number of Measurement Estimated Digit Significant Figures
14.8 m 3 ✓
$10.25 - ✓
0.05 L - ✓
1.000 g/mL - ✓
1.200 - ✓
6200 cm - ✓
403 kg - ✓
For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:
14.8 m: 15.0 m$10.25: $10.30.05 L: 0.050 L1.000 g/mL: 1.00 g/mL1.200: 1.206200 cm: 6200 cm403 kg: 400 kgNote that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.
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which set dose - 4/9 belong A integers B whole numbers C natural numbers D rational numbers
Answer:
-4/9 is a rational number
Step-by-step explanation:
Rational numbers are the numbers you can make by dividing one integer by another, so in other words a fraction.
Answer
4/9 belongs to rational numbers (D).
Explanation
(Lol moderator deleted everyone's answers so I'm gonna answer).
First I'll give you a definition of each choice.
Integers: Integers don't include decimals or fractions. Integers are positive and negative numbers. So basically it's this; (..., -3, -2, -1, 0, 1, 2, 3, ...). The '...' means numbers from infinity to the next number. I hope this makes sense Imao.
Whole numbers: whole numbers are integers, except they don't include negative numbers. Whole numbers include 0 (zero)... (0, 1, 2, 3, ...)
Natural numbers: natural numbers are whole numbers but they don't include 0 (zero)... (1, 2, 3, ...)
Rational numbers: rational numbers are numbers that can be expressed as a fraction. This includes repeating decimals such as 0.333 repeating. Rational numbers also include integers, because if you put the number over one, that is a fraction. Rational numbers are basically every number except for the radicals of some numbers (such as the square root of 3) and pi.
So now let's just see which one 4/9 is.
Well, 4/9 is not an integer, whole number, or natural number because it is a fraction.
But 4/9 can be expressed as a fraction (well, it already is one) meaning it is a rational number.
Help please will give brainliest to the first CORRECT answer
Answer:
part A: 4 batches of pancakes
part B: draw something this I think
400 STUDENTS OUT OF 2000 at a school are surveyed. 50 said they play a sport at the high school. Predict the
number of students in the population (the entire school) that would answer similarly.
25
2500
250
0.125
HURRY PLEASE!!!!!!!
Answer:250
Step-by-step explanation:
Sarah made a 72% on her science test. If she got 18 problems correct, how many questions were on the test?
Which is an equivalent form of the following equation?
2x – 3y = 3
Answer:
y=2/3x - 1
Step-by-step explanation:
2x-3y=3
-2x -2x
-3y= -2x + 3
÷-3 ÷-3 ÷-3
y= -2/3 x - 1
Central conservative forces: (a) Consider the force F= r2kr^ : Is this force conservative? Is it central? If it is conservative find the potential energy V(r). For full marks you need to justify your answer and explain any assumptions that you make.
The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force
To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.
A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:
∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.
Calculating the components of F = r^2k(r^):
Fx = 0, since there is no force component in the x-direction.
Fy = 0, since there is no force component in the y-direction.
Fz = r^2kr^.
Taking the partial derivatives, we have:
∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.
∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.
Substituting these values into the curl equation, we get:
∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).
Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.
Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).
For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.
Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.
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Alona bought 3 cans of paint for Php403 p er can. She gave the salesclerk Php1 500. How much change did she get?
6.) What is asked in the problem?
A. amount of her money
B. total amount of the paints
C. amount left in her money
D. amount of each can of paint
7. )What are the given facts?
A. Php1 500, Php403
B. 3 cans of paint, Php 403
C. Php1 500, Php403 and 3 cans of paints
D. 3 cans of paints, Php304 and Php1 500
8. )How much change did she get?
A. Php291 B. Php299 C. Php319 D. Php391
9.) Lilia has six Php100 bills, seven Php50 bills and eleven Php20 bills. How much does she have?
A. Php1 117 B. Php1 170 C. Php1 217 D. Php1 270
10.) Mang Jose is a tricycle driver. He charges Php10 for every passenger he transports. The tricycle carries 4 passengers each trip. How much does he earn for 21 trips?
A. Php804 B. Php814 C. Php834 D. Php840
Answer:
6) C. amount left in her money
7) C. Php1 500, Php403 and 3 cans of paints
8) A. Php291
9) B. Php1 170
10) D. Php840
Step-by-step explanation:
Alona bought 3 cans of paint for Php403 p er can. She gave the salesclerk Php1 500. How much change did she get?
6.) What is asked in the problem?
Aloha was asked of her change. This means the amount that is left after buying the 3 cans of paint. Hence, option C is correct.
C. amount left in her money
7. )What are the given facts?
The given facts in the question are
The 3 cans of paint that cost Php 403 and the amount she paid the clerk which is Php 1500
Hence, Option C. Is correct.
C. Php1 500, Php403 and 3 cans of paints
8. )How much change did she get?
The amount for change she got is calculated as.
Php 1 500 - 3(Php 403)
= Php 1 500 - Php 1 209
= Php 291
The amount of change she got is Php 291
Option A. Php291 is correct
9.) Lilia has six Php100 bills, seven Php50 bills and eleven Php20 bills. How much does she have?
The question above can be interpreted as:.
Six Php100 bills
= 6 (Php100)
= Php 600
Seven Php50 bills
7 (Php50)
= Php 350
Eleven Php20 bills
11 (Php20)
= Php 220
The amount she she has is calculated as:
Php 600 + Php 350 + Php 220
= Php 1 170
Hence, Option B. Php1 170 is correct
10.) Mang Jose is a tricycle driver. He charges Php10 for every passenger he transports. The tricycle carries 4 passengers each trip. How much does he earn for 21 trips?
We are told that:
He charges Php10 for every passenger he transports. The tricycle carries 4 passengers each trip.
Hence, the cost for each trip is
Php 10 × 4 passengers
= Php 40
Hence:
1 trip = Php 40
21 trips = x
Cross Multiply
x = 21 trips × Php 40
x = Php 840
Option D. Php840 is correct
b.The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank). c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time____ (mins) (enter the numbers only)
(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.
To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.
If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).
If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.
Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).
(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.
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Complete question:
The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.
(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).
c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)
Find the product 6 • (–9).
please i need this rn its urgent
Answer:
\( - 54\)
Step-by-step explanation:
it is too easy use your calculator!(-_-メ)
Answer:
-54
Step-by-step explanation:
When a number is decreased by -8 and the result is -20. What is the number? THANKS you for your help
Answer:
-12
Step-by-step explanation:
To decrease by -8 is to subtract, therefore x-8= -20. When you add 8 on both sides, the answer is -12.
what is s for the following function
Answer:
S = 3
S = 5
S = 7
S = 9
Step-by-step explanation:
t = 3s + 2
when t = 11
11 = 3s + 2
11 – 2 = 3s
9 = 3s
s = 3
t = 3s + 2
when t = 17
17 = 3s + 2
17 – 2 = 3s
15 = 3s
s = 5
t = 3s + 2
when t = 23
23 = 3s + 2
23 – 2 = 3s
21 = 3s
s = 7
t = 3s + 2
when t = 29
29 = 3s + 2
29 – 2 = 3s
27 = 3s
s = 9
I HOPE ALL THIS HELPS
RATE AS BRAINLIEST PLS
PLEASE RESPONDD!! IT'S TIMED :") The function f(x) = 4x – 0.1x^2 is used to model the
curve of a bridge over a small river, where x is the
distance from one side of the river and the x-axis
represents the ground. The mathematical range for the
function is the set of real numbers. Which statement describes the limitation for the reasonable range compared to the mathematical range?
Answer: it’s b
Step-by-step explanation:
Answer:
answer is B
Step-by-step explanation:
its b
"
Solve the initial value problem. {d y}/{d t}=5 t sin ^{2} y, y(1)={3 \pi}{4} The solution is
"
The solution to the initial value problem dy/dt = 5t sin^2(y) with y(1) = 3π/4 is given by y = (5/2)t^2 - π/4 - (5/2).
To solve the initial value problem dy/dt = 5t sin^2(y) with the initial condition y(1) = 3π/4, we can separate variables and then integrate both sides.
Step 1: Separate variables
dy/sin^2(y) = 5t dt
Step 2: Integrate both sides
∫dy/sin^2(y) = ∫5t dt
To integrate the left side, we can use a trigonometric identity. Let's rewrite sin^2(y) as (1 - cos^2(y)):
∫dy/(1 - cos^2(y)) = ∫5t dt
Now, let's use the identity sec^2(y) = 1 + tan^2(y) to further simplify the integral:
∫dy/(1 + tan^2(y)) = ∫5t dt
The integral on the left side is now in a form that can be evaluated easily. It is equal to arctan(tan(y)):
arctan(tan(y)) = (5/2)t^2 + C
Step 3: Solve for y
Since y(1) = 3π/4, we can substitute this value into the equation:
arctan(tan(3π/4)) = (5/2)(1)^2 + C
arctan(-1) = (5/2) + C
Now, we can solve for C:
C = arctan(-1) - (5/2)
C = -π/4 - (5/2)
Step 4: Substitute C back into the equation
Now we can substitute the value of C back into the equation to find the solution:
arctan(tan(y)) = (5/2)t^2 - π/4 - (5/2)
Since arctan(tan(y)) is equal to y, we have:
y = (5/2)t^2 - π/4 - (5/2)
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Solve the initial value problem. {d y}/{d t}=5 t sin ^{2} y, y(1)={3 \pi}{4} What is the solution?
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ
The two digits differ by 3.
Let's assume that the original two-digit positive integer is represented as "10a + b," where 'a' represents the tens digit and 'b' represents the units digit.
According to the problem, when the digits are reversed, the resulting integer is "10b + a."
The difference between the original integer and the reversed integer is given as 27.
Mathematically, we can express this as:
(10a + b) - (10b + a) = 27.
Simplifying the equation, we get:
9a - 9b = 27,
9(a - b) = 27.
Dividing both sides by 9, we have:
a - b = 3.
Therefore, the difference between the two digits is 3.
To verify, let's consider an example.
If the original two-digit positive integer is 54, reversing the digits gives us 45.
The difference between 54 and 45 is indeed 27, and the difference between the two digits is 5 - 4 = 1, which confirms that the difference is 3.
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Estimate the square root. Round to the nearest integer.
V56
Plz help I’m getting timed
Need help, due ASAP. Please help.
Answer:
a = 36.37 cm
c = 18.19 cm
Step-by-step explanation:
to find a, use tan
⇒ tan = \(\frac{opposite}{adjacent}\)
⇒ tan 60 = \(\frac{21}{a}\)
tan of 60 is 1.732
⇒ 1.732 = \(\frac{21}{a}\)
multiply 21 on both sides
⇒ 1.732 x 21 = \(\frac{21}{a}\)x 21
⇒ 36.37 = a
to find c, use sine
⇒ sine = \(\frac{oppsosite}{hypotenuse}\)
⇒ sine 60 = \(\frac{21}{c}\)
sine of 60 is 0.866
⇒ 0.866 = \(\frac{21}{c}\)
muliply 21 on both sides
⇒ 0.866 x 21 = \(\frac{21}{c}\) x 21
⇒ 18.19 = c
Help will mark brainliest!
By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:
x = 11m∠B = 108°m∠B = 36°m∠D = 36°How to find the value of x?Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:
m∠B + m∠C + m∠D = 180°
Then:
13x - 35 + 5x - 19 + 2x + 14 =180
20x -40 = 180
20x = 180 + 40
20x = 220
x = 220/20
x = 11
Now that we know the value of x, we can find the measures of the angles.
m∠B = (13x- 35)° = (13*11 - 35)° = 108°
m∠B = (5x - 19)° = (5*11 - 19)° = 36°
m∠D = (2x + 14)° = (2*11 + 14)° = 36°
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to construct a confidence interval using matched pairs, we must compute the standard deviation of the
We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated.
The complete question is:
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?
The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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PLEASE HELP
A random sample of 50 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.
Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 10 18 15 7
Which graphical representation would be best to display the data?
Box plot
Line plot
Histogram
Stem-and-leaf plot
The graphical representation that would be best to display the data is given as follows:
Histogram.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
The four types of products are given as follows:
Health and Medicine.Beauty.Household.Grocery.Each of these item would represent a bin, and the values of each bin are given as follows:
Health and Medicine: 10.Beauty: 18.Household: 15.Grocery: 7.More can be learned about histograms at brainly.com/question/25983327
Idil drove 12 miles in 1/5 of an hour. On average how fast did she drive in miles per hour
If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.
To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):
Average speed = distance ÷ time
Average speed = 12 miles ÷ (1/5) hour
To divide by a fraction, we can multiply by its reciprocal, so:
Average speed = 12 miles × 5/1 hour
Average speed = 60 miles per hour
Therefore, Idil drove at an average speed of 60 miles per hour.
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A population of 350 animals has a growth rate of 5% each year. Write an exponential function to model this situation.
Given:
The population of animals = 350
Growth rate = 5% each year.
To find:
The exponential function to model this situation.
Solution:
The general exponential growth model is:
\(f(t)=a(1+r)^t\)
Where, a is the initial value, r is the growth rate in decimal and t is the time period.
Substituting \(a=350, r=0.05\) in the above formula, we get
\(f(t)=350(1+0.05)^t\)
\(f(t)=350(1.05)^t\)
Therefore, the required exponential function is \(f(t)=350(1.05)^t\), where f(t) is the number of animals after t years.
In an ecological study, the sampling mean proportion is 0.28 and the sample size is 50. What is the margin of error with a confidence level of 95%?
The margin of error is 0.1245 (approx) with a confidence level of 95%.
What is margin of error ?Margin of error is a statistic which is expressing the measurement of random sampling error in the results of a survey.
Margin of error = \(z^{*}\)\(\sqrt{\frac{p(1-p)}{n} }\)
where \(z^{*}\) is the value for confidence level or quantile,
p is the sampling mean proportion and n is the sample size.
How to find margin of error in given problem ?Here, The sampling mean proportion(p)= 0.28
The sample size(n)= 50
Confidence level = 95%
Hence Value for 95% confidence level (\(z^{*}\))= 1.96
∴ Margin of error = \(1.96\)\(\sqrt{\frac{0.28(1-0.28)}{50} }\)
= \(1.96\)\(\sqrt{\frac{0.28*0.72}{50} }\)
= \(1.96\sqrt{\frac{0.2016}{50} }\)
= \(1.96\sqrt{0.004032}\)
= \(1.96\)×\(0.0635\)
= \(0.1245\) (approx)
So, The margin of error is 0.1245 (approx).
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Which of the following is the reciprocal of 1/5 ?
answers
5
1/5 5/5 1
Answer:
5
Step-by-step explanation:
A reciprocal is the inverse of a fraction.
To find it just flip the numerator and denominator.
1/5 becomes 5/1, or 5.
The calculated reciprocal of the number 1/5 is 5
How to determine the reciprocal of the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 1/5
By definition, the reciprocal of a number x is represebted as
reciprocal = 1/x
In this case,
x = 1/5
Substitute the known values in the above equation, so, we have the following representation
reciprocal = 1/(1/5)
Evaluate
reciprocal = 5
Hence, the reciprocal is 5
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Find the equation for the plane through the points Po(1.-5, -5). Q(-3,- 2, -1), and Role-5,3,0) Using a coefficient of - 17 for x, the equation of the plane is (Type an equation.)
The equation for a plane can be written in the form ax + by + cz = d, where a, b, and c are the coefficients of x, y, and z, respectively, and d is a constant.
To find the equation for the plane through the given points, we first need to find two vectors that lie in the plane. We can do this by subtracting one point from another:
v1 = Q - Po = (-3, -2, -1) - (1, -5, -5) = (-4, 3, 4)
v2 = Ro - Po = (-5, 3, 0) - (1, -5, -5) = (-6, 8, 5)
Now we can find the normal vector to the plane by taking the cross product of v1 and v2:
n = v1 x v2 = (-4, 3, 4) x (-6, 8, 5) = (-44, -4, 36)
The coefficients of x, y, and z in the equation of the plane are simply the components of the normal vector:
-44x - 4y + 36z = d
To find the value of d, we can substitute one of the points into the equation and solve for d:
-44(1) - 4(-5) + 36(-5) = d
d = -444
So the equation of the plane, using a coefficient of -17 for x, is:
-17x + 2y - 2z = 74
To find the equation of the plane through points P(1, -5, -5), Q(-3, -2, -1), and R(0, -5, 3), we first need to find two vectors in the plane, then compute their cross product to get the normal vector of the plane.
Vectors PQ and PR can be found as follows:
PQ = Q - P = <-3 - 1, -2 - (-5), -1 - (-5)> = <-4, 3, 4>
PR = R - P = <0 - 1, -5 - (-5), 3 - (-5)> = <-1, 0, 8>
Now, compute the cross product of PQ and PR:
N = PQ × PR = <3 * 8 - 4 * 0, -(-1 * 8 - 4 * 4), -1 * 0 - 4 * 3> = <24, 24, -12>
We are given that the coefficient of x is -17, so we need to scale the normal vector to get the desired coefficient. The scaling factor is:
-17 / N_x = -17 / 24
Scaled normal vector: <-17, -17, 8.5>
Now, we can use the scaled normal vector and the coordinates of P to find the equation of the plane:
-17(x - 1) - 17(y + 5) + 8.5(z + 5) = 0
Thus, the equation of the plane is:
-17x - 17y + 8.5z = 42.5
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